Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22590564 | C2 | semidirect |
| 2. #22587729 | C2 | semidirect |
| 4. #22586412 | C2 | semidirect |
| 5. #22586394 | C2 | semidirect |
| 6. #22586387 | C2 | semidirect |
| 7. D4×C16×C71 | C2 | semidirect |
| 115. D4×C16 | D71 | semidirect |
| 121. C71 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590564 | 2 |
| #22587729 | 2 |
| #22587695 | 2 |
| #22586412 | 2 |
| #22586394 | 2 |
| #22586387 | 2 |
| D4×C16×C71 | 2 |
| #12467 | 71 |